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Chapter 6: Problem 71

Write as a percent. If necessary, round to the nearest tenth of a percent. $$\frac{4}{9}$$

Short Answer

Expert verified
The fraction \(\frac{4}{9}\) as a percent, rounded to the nearest tenth, is 44.4%.

Step by step solution

01

Convert Fraction to Decimal

First, divide the numerator (4) by the denominator (9) to get a decimal. This could be done with a calculator or manually. This yields 0.4444...
02

Convert Decimal to Percentage

Now to convert this decimal number to a percentage, we have to multiply it by 100. Doing this gives us 44.44... percent.
03

Rounding

The instruction requires rounding to the nearest tenth of a percent if necessary. Therefore, we round 44.44... percent to 44.4 percent.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fraction to Decimal
Converting a fraction to a decimal is the first step in turning it into a percentage. To do this, the numerator (the top part of the fraction) is divided by the denominator (the bottom part of the fraction). For example, with the fraction \(\frac{4}{9}\), you divide 4 by 9. This division can either be done manually through long division or with a calculator. You might see a repeating decimal like 0.4444..., which means the digit 4 repeats indefinitely. Seeing a repeating decimal is common when the denominator does not neatly divide the numerator.
Decimal to Percentage
Once you have a decimal, converting it to a percentage is straightforward. You multiply the decimal by 100 to shift the decimal point two places to the right. This is because 'percent' literally means 'per one hundred'.
  • If your decimal is 0.4444... from the previous division, multiplying it by 100 gives you 44.44...
  • You achieve this by performing: \(0.4444... \times 100 = 44.44...\)
Turning decimals to percentages helps you express parts of a whole in a more relatable way, as percentages are commonly used in daily life.
Rounding Percentages
Rounding is an essential step when percentages are required to be accurate to a certain decimal place. In many cases, percentages are rounded to the nearest tenth, hundredth, or whole percent. Rounding involves deciding whether to stay at the current tenth or move up to the next.
  • Look at the second decimal place (hundredths) to decide if rounding is needed. In our example, with 44.44..., we observe the second digit after the decimal, which is 4.
  • If this digit is 5 or more, you'd round up, but since it's less than 5, you round down, keeping the tenth place as is.
  • Thus, 44.44... percent rounds down to 44.4 percent.
Rounding makes numerical information easier to comprehend and is especially useful when precision beyond a certain point is unnecessary.

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